Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×#4508 |
| Fitting | C2×C32×C16 ⋊ C2 |
| Sylow | C32 ⋊ #350 |
126 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#350, C2×C3×#4508, D3×#4508, … |
| maximal normal subgroup of | C3×D3×#350, C2×C3×#4508, D3×#4508, … |
| maximal quotient of | C3×#67523, C3×#67525, C3×#67503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1134);